Question

extra practice: angle relationships
do now
directions. answer the following questions. show all your work.
1.) use the diagram to solve for x.

1. if m∠eod = 60° and ∠aoe is a right angle, what are the values of m∠doc and m∠boc?

Explanation:

Step1: Identify angle - pair relationship for the first question

Vertical angles are equal. So $x - 35=142$.

Step2: Solve for x in the first - question

Add 35 to both sides of the equation $x-35 = 142$. We get $x=142 + 35=177$.

Step3: Analyze angles for the second question

Since $\angle AOE$ is a right - angle ($90^{\circ}$) and $\angle EOD = 60^{\circ}$, and $\angle AOE+\angle EOD+\angle DOC=180^{\circ}$ (a straight - line angle).

Step4: Calculate $\angle DOC$

$\angle DOC=180^{\circ}-\angle AOE-\angle EOD$. Substitute $\angle AOE = 90^{\circ}$ and $\angle EOD = 60^{\circ}$, we have $\angle DOC=180-(90 + 60)=30^{\circ}$.

Step5: Calculate $\angle BOC$

$\angle BOC$ and $\angle EOD$ are vertical angles. So $\angle BOC=\angle EOD = 60^{\circ}$.

Answer:

1. $x = 177$
2. $m\angle DOC = 30^{\circ}$, $m\angle BOC = 60^{\circ}$